Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#443 ⋊ C2 |
| Sylow | C13 ⋊ #2955 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^d=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #16016155, #16016157, #16016162, … |
| maximal normal subgroup of | #16016155, #16016157, #16016162, … |
| maximal quotient of | C8×#88165, C8×#88168, C8×#88169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13408);